l = 4w - 15

Perimeter = 2l + 2w

Substitute, we get:

400 = 2(4w - 15) + 2w

400 = 8w - 30 + 2w

10w - 30 = 400

Add 30 to each side

10w = 370

Divide each side by 10 to isolate w

w = 37

Plug that back into our original equation to find l

l = 4(37) - 15

l = 148 - 15

l = 133

So we have (l, w) = (37, 133)